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njwildberger.com | ||
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carcinisation.com
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| | | | | Gödel's theorems say something important about the limits of mathematical proof. Proofs in mathematics are (among other things) arguments. A typical mathematical argument may not be "inside" the universe it's saying something about. The Pythagorean theorem is a statement about the geometry of triangles, but it's hard to make a proof of it using nothing... | |
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cre8math.com
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| | | | | This might sound like an odd question -- most students seem to think so when I ask it. The reason it sounds a little strange is that most students -- even when I taught at a magnet STEM high school -- think there's just one type of geometry: Euclidean geometry. This isn't surprising given the... | |
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notageni.us
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| | | | | Most people in modern society have been trained in arithmetic and algebra from childhood, but don't often know what math is. The Basis of Math Every concept in math is a precisely parsed concept in an imaginary space. While some numbers represent real things (e.g., 2, 3) and are therefore called "real numbers", others can [...]Read More... from Defining Math | |
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fabricebaudoin.blog
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| | | In this section, we consider a diffusion operator $latex L=\sum_{i,j=1}^n \sigma_{ij} (x) \frac{\partial^2}{ \partial x_i \partial x_j} +\sum_{i=1}^n b_i (x)\frac{\partial}{\partial x_i}, $ where $latex b_i$ and $latex \sigma_{ij}$ are continuous functions on $latex \mathbb{R}^n$ and for every $latex x \in \mathbb{R}^n$, the matrix $latex (\sigma_{ij}(x))_{1\le i,j\le n}$ is a symmetric and non negative matrix. Our... | ||
